Solve {l}{0.5x+4y=-1}{+2.5y=3.5}

$$\left. \begin{array} { l } { 0.5 x + 4 y = - 1 } \\ { + 2.5 y = 3.5 } \end{array} \right.$$

Solve for x, y

$$x=-13.2$$

$$y=1.4$$

Solution Steps

Consider the second equation. Divide both sides by 2.5.

$$y=\frac{3.5}{2.5}$$

Expand \frac{3.5}{2.5} by multiplying both numerator and the denominator by 10.

$$y=\frac{35}{25}$$

Reduce the fraction \frac{35}{25} to lowest terms by extracting and canceling out 5.

$$y=\frac{7}{5}$$

Consider the first equation. Insert the known values of variables into the equation.

$$0.5x+4\times \frac{7}{5}=-1$$

Multiply 4 and \frac{7}{5} to get \frac{28}{5}.

$$0.5x+\frac{28}{5}=-1$$

Subtract \frac{28}{5} from both sides.

$$0.5x=-1-\frac{28}{5}$$

Subtract \frac{28}{5} from -1 to get -\frac{33}{5}.

$$0.5x=-\frac{33}{5}$$

Divide both sides by 0.5.

$$x=\frac{-\frac{33}{5}}{0.5}$$

Express \frac{-\frac{33}{5}}{0.5} as a single fraction.

$$x=\frac{-33}{5\times 0.5}$$

Multiply 5 and 0.5 to get 2.5.

$$x=\frac{-33}{2.5}$$

Expand \frac{-33}{2.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{-330}{25}$$

Reduce the fraction \frac{-330}{25} to lowest terms by extracting and canceling out 5.

$$x=-\frac{66}{5}$$

The system is now solved.

$$x=-\frac{66}{5} y=\frac{7}{5}$$